How is the gambler’s fallacy not a logical paradox? A flipped coin coming up heads 25 times in a row has odds in the millions, but if you flip heads 24 times in a row, the 25th flip still has odds of exactly 0.5 heads. Isn’t there something logically weird about that?

Question

I know it’s true, it’s just something that seems hard to wrap my head around. How is this not a logical paradox?

In: Mathematics

Answer 1

No. Think about it like this. Take any coin. I have a Roman coin from CE 156. I’m going to flip it once. What are the odds of it being heads? 50:50 – easy, right? Wouldn’t it be weird if the odds of that one flip depended on how many times the coin had been flipped in the past and whether it came up heads or tails each time?